Parameter estimation in non-linear mixed effects models with SAEM algorithm: extension from ODE to PDE

This Research Report is now published in the Journal: ESAIM: Mathematical Modelling and Numerical Analysis. DOI: http://dx.doi.org/10.1051/m2an/2013140 and its updated associated version is also available on HAL at: http://hal.archives-ouvertes.fr/hal-00936373 Parameter estimation in non linear mixed effects models requires a large number of evaluations of the model to study. For ordinary differential equations, the overall computation time remains reasonable. However when the model itself is complex (for instance when it is a set of partial differential equations) it may be time consuming to evaluate it for a single set of parameters. The procedures of populational parametrization (for instance using SAEM algorithms) are then very long and in some cases impossible to do within a reasonable time. We propose here a very simple methodology which may accelerate populational parametrization of complex models, including partial differential equations models. We illustrate our method on the classical KPP equation